The goldstino is the Nambu−Goldstone fermion emerging in the spontaneous breaking of supersymmetry. It is the close fermionic analog of the Nambu−Goldstone boson controlling the spontaneous breakdown of ordinary bosonic symmetry.
As in the case of Goldstone bosons, it is massless, unless there is also a small explicit supersymmetry breakdown involved, on top of the basic spontaneous breakdown, in which case it develops a small mass—see Pseudo-Goldstone boson.
In theories where supersymmetry is a global symmetry, the goldstino is an ordinary particle (possibly the lightest supersymmetric particle, responsible for dark matter). In theories where supersymmetry is a local symmetry, the goldstino is absorbed by the gravitino, the gauge field it couples to, becoming its longitudinal component, and giving it nonvanishing mass. This mechanism is a close analog of the way the Higgs field gives nonzero mass to the W and Z bosons.
Vestigial bosonic superpartners of the goldstinos, called sgoldstinos, might also appear, but need not, as supermultiplets have been reduced to arrays. In effect, SSB of supersymmetry, by definition, implies a nonlinear realization of the supersymmetry in the Nambu−Goldstone mode, in which the goldstino couples identically to all particles in these arrays, and is thus the superpartner of all of them, equally.